A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
SIAM Journal on Computing
On-line bin packing in linear time
Journal of Algorithms
An on-line algorithm for variable-sized bin packing
Acta Informatica
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Improved space for bounded-space, on-line bin-packing
SIAM Journal on Discrete Mathematics
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems
Journal of the ACM (JACM)
New Algorithms for Bin Packing
Journal of the ACM (JACM)
On the online bin packing problem
Journal of the ACM (JACM)
An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing
SIAM Journal on Discrete Mathematics
Resource augmentation for online bounded space bin packing
Journal of Algorithms
New Bounds for Variable-Sized Online Bin Packing
SIAM Journal on Computing
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Optimal online bounded space multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for on-line bin-packing problems with cardinality constraints
Discrete Applied Mathematics
ACM SIGACT News
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
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We consider a one dimensional storage system where each container can store a bounded amount of capacity as well as a bounded number of items k ≥ 2. This defines the (standard) bin packing problem with cardinality constraints which is an important version of bin packing, introduced by Krause, Shen and Schwetman already in 1975. Following previous work on the unbounded space online problem, we establish the exact best competitive ratio for bounded space online algorithms for every value of k. This competitive ratio is a strictly increasing function of k which tends to ${\it \Pi}_{\infty}+1\approx 2.69103$ for large k. Lee and Lee showed in 1985 that the best possible competitive ratio for online bounded space algorithms for the classical bin packing problem is the sum of a series, and tends to ${\it \Pi}_{\rm \infty}$ as the allowed space (number of open bins) tends to infinity. We further design optimal online bounded space algorithms for variable sized bin packing, where each allowed bin size may have a distinct cardinality constraint, and for the resource augmentation model. All algorithms achieve the exact best possible competitive ratio possible for the given problem, and use constant numbers of open bins. Finally, we introduce unbounded space online algorithms with smaller competitive ratios than the previously known best algorithms for small values of k, for the standard cardinality constrained problem. These are the first algorithms with competitive ratio below 2 for k = 4,5,6.